The Pressure-Streamfunction MFS Formulation for the Detection of an Obstacle Immersed in a Two-Dimensional Stokes Flow

Abstract

In this paper we consider a geometric inverse problem which requires detecting an unknown obstacle such as a submarine or an aquatic mine immersed in a Stokes slow viscous stationary flow of an incompressible fluid, from a single set of Cauchy (fluid velocity and stress force) boundary measurements. The numerical reconstruction is based on the method of fundamental solutions (MFS) for the pressure and streamfunction in two dimensions combined with regularization. Numerical results are presented and discussed.